quiz+2+solution - This means that for large trees there...

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ChBE3200 Pop quiz II Your name: ________SOLUTION____________________ 1. Plants (height L) are known to transport water by capillary action through capillaries or ducts (diameter ~d) in the stems to the leaves far away from the roots. (a) Come up with a dimensionless number “Pl” that describes the relative importance of capillary action and gravity. (Hint: surface tension γ has units of force per length.) Pl = γ d/mg = γ d/[( π d 2 /4)L ρ g] (b) For a tall tree, would Pl be large or small? Small because L is large. (c) Assuming the same surface tension of water in tall trees and small plants, what does this imply? Large Pl for tall trees implies that the capillary force is not large enough to pull water to the top of the plants or to the branches and leaves.
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Unformatted text preview: This means that for large trees there must be some other mechanism(s) to transport water. 2. Use Reynolds number to describe (qualitatively) how momentum is transferred when a person swims in syrup (speed ~1 m/s, syrup density ~ 2000 kg/m 3 , viscosity ~10 Pa.sec, and a person is ~ 0.25 m “thick”) and when a bacterium swims in water (speed ~10-6 m/s, water density ~ 1000 kg/m 3 , viscosity ~0.001 Pa.sec, and a bacterium is ~ 10-6 m). Can the flow be turbulent in either case? Re (person) = ρ vL/ μ = (2000) (1) (0.25) / (10) = 100 Momentum transfer dominated by inertial effect. Still laminar flow. Re (bacterium) = ρ vL/ μ = (1000) (10-6 ) (10-6 ) / (0.001) = 10-6 Momentum transfer dominated by viscous effect. Definitely laminar flow....
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